eBook of George Grote, Aristotle

It is impossible, however, for a man to believe that one contrary is predicable of its contrary, or that one contrary is identical with its contrary, essentially and as an universal proposition; though he may believe that it is so by accident (i.e. in some particular case, by reason of the peculiarities of that case). In various ways this last is possible; but this we reserve for fuller examination.45

45 Analyt. Prior. II. xxi. p. 67, b. 23: ἀλλ’ ἴσως ἐκεῖνο ψεῦδος, τὸ ὑπολαβεῖν τινὰ κακῷ εἶναι τὸ ἀγαθῷ εἶναι, εἰ μὴ κατὰ συμβεβηκός· πολλαχῶς γὰρ ἐγχωρεῖ τοῦθ’ ὑπολαμβάνειν. ἐπισκεπτέον δὲ τοῦτο βέλτιον. This distinction is illustrated by what we read in Plato, Republic, v. pp. 478-479. The impossibility of believing that one contrary is identical with its contrary, is maintained by Sokrates in Plato, Theætetus, p. 190, B-D, as a part of the long discussion respecting ψευδὴς δόξα: either there is no such thing as ψευδὴς δόξα, or a man may know, and not know, the same thing, ibid. p. 196 C. Aristotle has here tried to show in what sense this last-mentioned case is possible.

Whenever (Aristotle next goes on to say) the extremes of a syllogism reciprocate or are co-extensive with each other (i.e. when the conclusion being affirmative is convertible simply), the middle term must reciprocate or be co-extensive with both.46 If there be four terms (A, B, C, D), such that A reciprocates with B, and C with D, and if either A or C must necessarily be predicable of every subject; then it follows that either B or D must necessarily also be predicable of every subject. Again, if either A or B must necessarily be predicable of every subject, but never both predicable of the same at once; and if, either C or D must be predicable of every subject, but never both predicable of the same at once; then, if A and C reciprocate, B and D will also reciprocate.47 When A is predicable of all B and all C, but of no other subject besides, and when B is predicable of all C, then A and B must reciprocate with each other, or be co-extensive with each other; that is, B may be predicated of every subject of which A can be predicated, though B cannot be predicated of A itself.48 Again, when A and B are predicable of all C, and when C reciprocates with B, then A must also be predicable of all B.49

46 Ibid. II. xxii. p. 67, b. 27, seq. In this chapter Aristotle introduces us to affirmative universal propositions convertible simpliciter; that is, in which the predicate must be understood to be distributed as well as the subject. Here, then, the quantity of the predicate is determined in thought. This is (as Julius Pacius remarks, p. 371) in order to lay down principles for the resolution of Induction into Syllogism, which is to be explained in the next chapter. In these peculiar propositions, the reason urged by Sir W. Hamilton for his favourite precept of verbally indicating the quantity of the predicate, is well founded as a fact: though he says that in all propositions the quantity of the predicate is understood in thought, which I hold to be incorrect.

We may remark that this recognition by Aristotle of a class of universal affirmative propositions in which predicate and subject reciprocate, contrived in order to force Induction into the syllogistic framework, is at variance with his general view both of reciprocating propositions and of Induction. He tells us (Analyt. Post. I. iii. p. 73, a. 18) that such reciprocating propositions are very rare, which would not be true if they are taken to represent every Induction; and he forbids us emphatically to annex the mark of universality to the predicate; which he has no right to do, if he calls upon us to reason on the predicate as distributed (Analyt. Prior. I. xxvii., p. 43, b. 17; De Interpret. p. 17, b. 14).

47 Ibid. II. xxii. p. 68, a. 2-15.

48 Ibid. a. 16-21. πλὴν αὐτοῦ τοῦ A. Waitz explains these words in his note (p. 531): yet I do not clearly make them out; and Alexander of Aphrodisias declared them to assert what was erroneous (ἐσφάλθαι λέγει, Schol. p. 194, a. 40, Brandis).

49 Ibid. II. xxii. p. 68, a. 21-25.

Lastly, suppose two pairs of opposites, A and B, C and D; let A be more eligible than B, and D more eligible than C. Then, if A C is more eligible than B D, A will also be more eligible than D. For A is as much worthy of pursuit as B is worthy of avoidance, they being two opposites; the like also respecting C and D. If then A and D are equally worthy of pursuit, B and C are equally worthy of avoidance; for each is equal to each. Accordingly the two together, A C, will be equal to the two together, B D. But this would be contrary to the supposition; since we assumed A to be more eligible than B, and D to be more eligible than C. It will be seen that on this supposition A is more worthy of pursuit than D, and that C is less worthy of avoidance than B; the greater good and the lesser evil being more eligible than the lesser good and the greater evil. Now apply this to a particular case of a lover, so far forth as lover. Let A represent his possession of those qualities which inspire reciprocity of love towards him in the person beloved; B, the absence of those qualities; D, the attainment of actual sexual enjoyment; C, the non-attainment thereof. In this state of circumstances, it is evident that A is more eligible or worthy of preference than D. The being loved is a greater object of desire to the lover qua lover than sexual gratification; it is the real end or purpose to which love aspires; and sexual gratification is either not at all the purpose, or at best only subordinate and accessory. The like is the case with our other appetites and pursuits.50

50 Analyt. Prior. II. xxii. p. 68, a. 25-b. 17. Aristotle may be right in the conclusion which he here emphatically asserts; but I am surprised that he should consider it to be proved by the reasoning that precedes.

It is probable that Aristotle here understood the object of ἔρως (as it is conceived through most part of the Symposion of Plato) to be a beautiful youth: (see Plato, Sympos. pp. 218-222; also Xenophon, Sympos. c. viii., Hiero, c. xi. 11, Memorab. I. ii. 29, 30). Yet this we must say — what the two women said when they informed Simætha of the faithlessness of Delphis (Theokrit. Id. ii. 149) —

Κᾖπέ μοι ἄλλα τε πολλά, καὶ ὡς ἄρα Δέλφις ἔραται·
Κᾔτε μιν αὖτε γυναικὸς ἔχει πόθος, εἴτε καὶ ἀνδρός,
Οὐκ ἔφατ’ ἀτρεκὲς ἴδμεν.

Such is the relation of the terms of a syllogism in regard to reciprocation and antithesis. Let it next be understood that the canons hitherto laid down belong not merely to demonstrative and dialectic syllogisms, but to rhetorical and other syllogisms also; all of which must be constructed in one or other of the three figures. In fact, every case of belief on evidence, whatever be the method followed, must be tested by these same canons. We believe everything either through Syllogism or upon Induction.51

51 Ibid. II. xxiii. p. 68, b. 13: ἅπαντα γὰρ πιστεύομεν ἢ διὰ συλλογισμοῦ ἢ ἐξ ἐπαγωγῆς.

Though Aristotle might seem, even here, to have emphatically contrasted Syllogism with Induction as a ground of belief, he proceeds forthwith to indicate a peculiar form of Syllogism which may be constructed out of Induction. Induction, and the Syllogism from or out of Induction (he says) is a process in which we invert the order of the terms. Instead of concluding from the major through the middle to the minor (i.e. concluding that the major is predicable of the minor), we now begin from the minor and conclude from thence through the middle to the major (i.e. we conclude that the major is predicable of the middle).52 In Syllogism as hitherto described, we concluded that A the major was predicable of C the minor, through the middle B; in the Syllogism from Induction we begin by affirming that A the major is predicable of C the minor; next, we affirm that B the middle is also predicable of C the minor. The two premisses, standing thus, correspond to the Third figure of the Syllogism (as explained in the preceding pages) and would not therefore by themselves justify anything more than a particular affirmative conclusion. But we reinforce them by introducing an extraneous assumption:— That the minor C is co-extensive with the middle B, and comprises the entire aggregate of individuals of which B is the universal or class-term. By reason of this assumption the minor proposition becomes convertible simply, and we are enabled to infer (according to the last preceding chapter) an universal affirmative conclusion, that the major term A is predicable of the middle term B. Thus, let A (the major term) mean the class-term, long-lived; let B (the middle term) mean the class-term, bile-less, or the having no bile; let C (the minor term) mean the individual animals — man, horse, mule, &c., coming under the class-term B, bile-less.53 We are supposed to know, or to have ascertained, that A may be predicated of all C; (i.e. that all men, horses, mules, &c., are long-lived); we farther know that B is predicable of all C (i.e. that men, horses, mules, &c., belong to the class bile-less). Here, then, we have two premisses in the Third syllogistic figure, which in themselves would warrant us in drawing the particular affirmative conclusion, that A is predicable of some B, but no more. Accordingly, Aristotle directs us to supplement these premisses54 by the extraneous assumption or postulate, that C the minor comprises all the individual animals that are bile-less, or all those that correspond to the class-term B; in other words, the assumption, that B the middle does not denote any more individuals than those which are covered by C the minor — that B the middle does not stretch beyond or overpass C the minor.55 Having the two premisses, and this postulate besides, we acquire the right to conclude that A is predicable of all B. But we could not draw that conclusion from the premisses alone, or without the postulate which declares B and C to be co-extensive. The conclusion, then, becomes a particular exemplification of the general doctrine laid down in the last chapter, respecting the reciprocation of extremes and the consequences thereof. We thus see that this very peculiar Syllogism from Induction is (as indeed Aristotle himself remarks) the opposite or antithesis of a genuine Syllogism. It has no proper middle term; the conclusion in which it results is the first or major proposition, the characteristic feature of which it is to be immediate, or not to be demonstrated through a middle term. Aristotle adds that the genuine Syllogism, which demonstrates through a middle term, is by nature prior and more effective as to cognition; but that the Syllogism from Induction is to us plainer and clearer.56

52 Analyt. Prior. II. xxiii. p. 68, b. 15: ἐπαγωγὴ μὲν οὖν ἐστὶ καὶ ὁ ἐξ ἐπαγωγῆς συλλογισμὸς τὸ διὰ τοῦ ἑτέρου θάτερον ἄκρον τῷ μέσῳ συλλογίσασθαι· οἷον εἰ τῶν ΑΓ μέσον τὸ Β, διὰ τοῦ Γ δεῖξαι τὸ Α τῷ Β ὑπάρχον· οὕτω γὰρ ποιούμεθα τὰς ἐπαγωγάς.

Waitz in his note (p. 532) says: “Fit Inductio, cum per minorem terminum demonstratur medium prædicari de majore.” This is an erroneous explanation. It should have been: “demonstratur majorem prædicari de medio.” Analyt. Prior. II. xxiii. 68, b. 32: καὶ τρόπον τινὰ ἀντικεῖται ἡ ἐπαγωγὴ τῷ συλλογισμῷ· ὁ μὲν γὰρ διὰ τοῦ μέσου τὸ ἄκρον τῷ τρίτῳ δείκνυσιν, ἡ δὲ διὰ τοῦ τρίτου τὸ ἄκρον τῷ μέσῳ.

53 Ibid. II. xxiii. p. 68, b. 18: οἷον ἔστω τὸ Α μακρόβιον, τὸ δ’ ἐφ’ ᾧ Β, τὸ χολὴν μὴ ἔχον, ἐφ’ ᾧ δὲ Γ, τὸ καθ’ ἕκαστον μακρόβιον, οἷον ἄνθρωπος καὶ ἵππος καὶ ἡμίονος. τῷ δὴ Γ ὅλῳ ὑπάρχει τὸ Α· πᾶν γὰρ τὸ ἄχολον μακρόβιον· ἀλλὰ καὶ τὸ Β, τὸ μὴ ἔχειν χολήν, παντὶ ὑπάρχει τῷ Γ. εἰ οὖν ἀντιστρέφει τὸ Γ τῷ Β καὶ μὴ ὑπερτείνει τὸ μέσον, ἀνάγκη τὸ Α τῷ Β ὑπάρχειν.

I have transcribed this Greek text as it stands in the editions of Buhle, Bekker, Waitz, and F. Didot. Yet, notwithstanding these high authorities, I venture to contend that it is not wholly correct; that the word μακρόβιον, which I have emphasized, is neither consistent with the context, nor suitable for the point which Aristotle is illustrating. Instead of μακρόβιον, we ought in that place to read ἄχολον; and I have given the sense of the passage in my English text as if it did stand ἄχολον in that place.

I proceed to justify this change. If we turn back to the edition by Julius Pacius (1584, p. 377), we find the text given as follows after the word ἡμίονος (down to that word the text is the same): τῷ δὴ Γ ὅλῳ ὑπάρχει τὸ Α· πᾶν γὰρ τὸ Γ μακρόβιον· ἀλλὰ καὶ τὸ Β, τὸ μὴ ἔχον χολήν, παντὶ ὑπάρχει τῷ Γ. εἰ οὖν ἀντιστρέφει τὸ Γ τῷ Β, καὶ μὴ ὑπερτείνει τὸ μέσον, ἀνάγκη τὸ Α τῷ Β ὑπάρχειν. Earlier than Pacius, the edition of Erasmus (Basil. 1550) has the same text in this chapter.

Here it will be seen that in place of the words given in Waitz’s text, πᾶν γὰρ τὸ ἄχολον μακρόβιον, Pacius gives πᾶν γὰρ τὸ Γ μακρόβιον: annexing however to the letter Γ an asterisk referring to the margin, where we find the word ἄχολον inserted in small letters, seemingly as a various reading not approved by Pacius. And M. Barthélemy St. Hilaire has accommodated his French translation (p. 328) to the text of Pacius: “Donc A est à C tout entier, car tout C est longève.” Boethius in his Latin translation (p. 519) recognizes as his original πᾶν γὰρ τὸ ἄχολον μακρόβιον, but he alters the text in the words immediately preceding:— “Ergo toti B (instead of toti C) inest A, omne enim quod sine cholera est, longævum,” &c. (p. 519). The edition of Aldus (Venet. 1495) has the text conformable to the Latin of Boethius: τῷ δὴ Β ὅλῳ ὑπάρχει τὸ Α· πᾶν γὰρ τὸ ἄχολον μακρόβιον. Three distinct Latin translations of the 16th century are adapted to the same text, viz., that of Vives and Valentinus (Basil. 1542); that published by the Junta (Venet. 1552); and that of Cyriacus (Basil. 1563). Lastly, the two Greek editions of Sylburg (1587) and Casaubon (Lugduni 1590), have the same text also: τῷ δὴ Β ὅλῳ ὑπάρχει τὸ Α· πᾶν γὰρ [τὸ Γ] τὸ ἄχολον μακρόβιον. Casaubon prints in brackets the words [τὸ Γ] before τὸ ἄχολον.

Now it appears to me that the text of Bekker and Waitz (though Waitz gives it without any comment or explanation) is erroneous; neither consisting with itself, nor conforming to the general view enunciated by Aristotle of the Syllogism from Induction. I have cited two distinct versions, each different from this text, as given by the earliest editors; in both the confusion appears to have been felt, and an attempt made to avoid it, though not successfully.

Aristotle’s view of the Syllogism from Induction is very clearly explained by M. Barthélemy St. Hilaire in the instructive notes of his translation, pp. 326-328; also in his Preface, p. lvii.:— “L'induction n’est au fond qu’un syllogisme dont le mineur et le moyen sont d’extension égale. Du reste, il n’est qu’une seule manière dont le moyen et le mineur puissent être d’égale extension; c’est que le mineur se compose de toutes les parties dont le moyen représente la totalité. D’une part, tous les individus: de l’autre, l’espèce totale qu’ils forment. L’intelligence fait aussitôt équation entre les deux termes égaux.”

According to the Aristotelian text, as given both by Pacius and the others, A, the major term, represents longævum (long-lived, the class-term or total); B, the middle term, represents vacans bile (bile-less, the class-term or total); C, the minor term, represents the aggregate individuals of the class longævum, man, horse, mule, &c.

Julius Pacius draws out the Inductive Syllogism, thus:—

1. Omnis homo, equus, asinus, &c., est longævus.
2. Omnis homo, equus, asinus, &c., vacat bile.
Ergo:
3. Quicquid vacat bile, est longævum.

Convertible into a Syllogism in Barbara:—

1. Omnis homo, equus, asinus, &c., est longævus.
2. Quicquid vacat bile, est homo, equus, asinus, &c.
Ergo:
3. Quicquid vacat bile, est longævum.

Here the force of the proof (or the possibility, in this exceptional case, of converting a syllogism in the Third figure into another in Barbara of the First figure) depends upon the equation or co-extensiveness (not enunciated in the premisses, but assumed in addition to the premisses) of the minor term C with the middle term B. But I contend that this is not the condition peremptorily required, or sufficient for proof, if we suppose C the minor term to represent omne longævum. We must understand C the minor term to represent omne vacans bile, or quicquid vacat bile: and unless we understand this, the proof fails. In other words, homo, equus, asinus, &c. (the aggregate of individuals), must be co-extensive with the class-term bile-less or vacans bile: but they need not be co-extensive with the class-term long-lived or longævum. In the final conclusion, the subject vacans bile is distributed; but the predicate longævum is not distributed; this latter may include, besides all bile-less animals, any number of other animals, without impeachment of the syllogistic proof.

Such being the case, I think that there is a mistake in the text as given by all the editors, from Pacius down to Bekker and Waitz. What they give, in setting out the terms of the Aristotelian Syllogism from Induction, is: ἔστω τὸ Α μακρόβιον, τὸ δ’ ἐφ’ ᾧ Β, τὸ χολην μὴ ἔχον, ἐφ’ ᾧ δὲ Γ, τὸ καθ’ ἕκαστον μακρόβιον, οἷον ἄνθρωπος καὶ ἵππος καὶ ἡμίονος. Instead of which the text ought to run, ἐφ’ ᾧ δὲ Γ, τὸ καθ’ ἕκαστον ἄχολον, οἷον ἄνθρ. κ. ἵπ. κ. ἡμί. That these last words were the original text, is seen by the words immediately following: τῷ δὴ Γ ὅλῳ ὑπάρχει τὸ Α. πᾶν γὰρ τὸ ἄχολον μακρόβιον. For the reason thus assigned (in the particle γάρ) is irrelevant and unmeaning if Γ designates τὸ καθ’ ἕκαστον μακρόβιον, while it is pertinent and even indispensable if Γ designates τὸ καθ’ ἕκαστον ἄχολον. Pacius (or those whose guidance he followed in his text) appears to have perceived the incongruity of the reason conveyed in the words πᾶν γὰρ τὸ ἄχολον μακρόβιον; for he gives, instead of these words, πᾶν γὰρ τὸ Γ μακρόβιον. In this version the reason is indeed no longer incongruous, but simply useless and unnecessary; for when we are told that A designates the class longævum, and that Γ designates the individual longæva, we surely require no reason from without to satisfy us that A is predicable of all Γ. The text, as translated by Boethius and others, escapes that particular incongruity, though in another way, but it introduces a version inadmissible on other grounds. Instead of τῷ δὴ Γ ὅλῳ ὑπάρχει τὸ Α, πᾶν γὰρ τὸ ἄχολον μακρόβιον, Boethius has τῷ δὴ Β ὅλῳ ὑπάρχει τὸ Α, πᾶν γὰρ τὸ ἄχολον μακρόβιον. This cannot be accepted, because it enunciates the conclusion of the syllogism as if it were one of the premisses. We must remember that the conclusion of the Aristotelian Syllogism from Induction is, that A is predicable of B, one of the premisses to prove it being that A is predicable of the minor term C. But obviously we cannot admit as one of the premisses the proposition that A may be predicated of B, since this proposition would then be used as premiss to prove itself as conclusion.

If we examine the Aristotelian Inductive Syllogism which is intended to conduct us to the final probandum, we shall see that the terms of it are incorrectly set out by Bekker and Waitz, when they give the minor term Γ as designating τὸ καθ’ ἕκαστον μακρόβιον. This last is not one of the three terms, nor has it any place in the syllogism. The three terms are:

1. A — major — the class-term or class μακρόβιον — longævum.
2. B — middle — the class term or class ἄχολον — bile-less.
3. C — minor — the individual bile-less animals, man, horse, &c.

There is no term in the syllogism corresponding to the individual longæva or long-lived animals; this last (I repeat) has no place in the reasoning. We are noway concerned with the totality of long-lived animals; all that the syllogism undertakes to prove is, that in and among that totality all bile-less animals are included; whether there are or are not other long-lived animals besides the bile-less, the syllogism does not pretend to determine. The equation or co-extensiveness required (as described by M. Barthélemy St. Hilaire in his note) is not between the individual long-lived animals and the class, bile-less animals (middle term), but between the aggregate of individual animals known to be bile-less and the class, bile-less animals. The real minor term, therefore, is (not the individual long-lived animals, but) the individual bile-less animals. The two premisses of the Inductive Syllogism will stand thus:—

Men, Horses, Mules, &c., are long-lived (major).
Men, Horses, Mules, &c., are bile-less (minor).

And, inasmuch as the subject of the minor proposition is co-extensive with the predicate (which, if quantified according to Hamilton’s phraseology, would be, All bile-less animals), so that the proposition admits of being converted simply, — the middle term will become the subject of the conclusion, All bileless animals are long-lived.

54 Analyt. Prior. II. xxiii. p. 68, b. 27: δεῖ δὲ νοεῖν τὸ Γ τὸ ἐξ ἁπάντων τῶν καθ’ ἕκαστον συγκείμενον· ἡ γὰρ ἐπαγωγὴ διὰ πάντων.

55 Analyt. Prior. II. xxiii. p. 68, p. 23: εἰ οὖν ἀντιστρέφει τὸ Γ τῷ Β, καὶ μὴ ὑπερτείνει τὸ μέσον, ἀνάγκη τὸ Α τῷ Β ὑπάρχειν.

Julius Pacius translates this: “Si igitur convertatur τὸ Γ cum B, nec medium excedat, necesse est τὸ Α τῷ Β inesse.” These Latin words include the same grammatical ambiguity as is found in the Greek original: medium, like τὸ μέσον, may be either an accusative case governed by excedat, or a nominative case preceding excedat. The same may be said of the other Latin translations, from Boethius downwards.

But M. Barthélemy St. Hilaire in his French translation, and Sir W. Hamilton in his English translation (Lectures on Logic, Vol. II. iv. p. 358, Appendix), steer clear of this ambiguity. The former says: “Si donc C est réciproque à B, et qu’il ne dépasse pas le moyen, il est nécessaire alors que A soit à B:” to the same purpose, Hamilton, l. c. These words are quite plain and unequivocal. Yet I do not think that they convey the meaning of Aristotle. In my judgment, Aristotle meant to say: “If then C reciprocates with B, and if the middle term (B) does not stretch beyond (the minor C), it is necessary that A should be predicable of B.” To show that this must be the meaning, we have only to reflect on what C and B respectively designate. It is assumed that C designates the sum of individual bile-less animals; and that B designates the class or class-term bile-less, that is, the totality thereof. Now the sum of individuals included in the minor (C) cannot upon any supposition overpass the totality: but it may very possibly fall short of totality; or (to state the same thing in other words) the totality may possibly surpass the sum of individuals under survey, but it cannot possibly fall short thereof. B is here the limit, and may possibly stretch beyond C; but cannot stretch beyond B. Hence I contend that the translations, both by M. Barthélemy St. Hilaire and Sir W. Hamilton, take the wrong side in the grammatical alternative admissible under the words καὶ μὴ ὑπερτείνει τὸ μέσον. The only doubt that could possibly arise in the case was, whether the aggregate of individuals designated by the minor did, or did not, reach up to the totality designated by the middle term; or (changing the phrase) whether the totality designated by the middle term did, or did not, stretch beyond the aggregate of individuals designated by the minor. Aristotle terminates this doubt by the words: “And if the middle term does not stretch beyond (the minor).” Of course the middle term does not stretch beyond, when the terms reciprocate; but when they do not reciprocate, the middle term must be the more extensive of the two; it can never be the less extensive of the two, since the aggregate of individuals cannot possibly exceed totality, though it may fall short thereof.

I have given in the text what I think the true meaning of Aristotle, departing from the translations of M. Barthélemy St. Hilaire and Sir W. Hamilton.

56 Analyt. Prior. II. xxiii. p. 68, b. 30-38: ἔστι δ’ ὁ τοιοῦτος συλλογισμὸς τῆς πρώτης καὶ ἀμέσου προτάσεως· ὧν μὲν γάρ ἐστι μέσον, διὰ τοῦ μέσου ὁ συλλογισμός, ὧν δὲ μή ἐστι, δι’ ἐπαγωγῆς. — φύσει μὲν οὖν πρότερος καὶ γνωριμώτερος ὁ διὰ τοῦ μέσου συλλογισμός, ἡμῖν δ’ ἐναργέστερος ὁ διὰ τῆς ἐπαγωγῆς.

From Induction he proceeds to Example. You here take in (besides the three terms, major, middle, and minor, of the Syllogism) a fourth term; that is, a new particular case analogous to the minor. Your purpose here is to show — not, as in the ordinary Syllogism, that the major term is predicable of the minor, but, as in the Inductive Syllogism — that the major term is predicable of the middle term; and you prove this conclusion, not (as in the Inductive Syllogism) through the minor term, but through the new case or fourth term analogous to the minor.57 Let A represent evil or mischievous; B, war against neighbours, generally; C, war of Athens against Thebes, an event to come and under deliberation; D, war of Thebes against Phokis, a past event of which the issue is known to have been signally mischievous. You assume as known, first, that A is predicable of D, i.e. that the war of Thebes against Phokis has been disastrous; next, that B is predicable both of C and of D, i.e. that each of the two wars, of Athens against Thebes, and of Thebes against Phokis, is a war of neighbours against neighbours, or a conterminous war. Now from the premiss that A is predicable of D, along with the premiss that B is predicable of D, you infer that A is predicable of the class B, or of conterminous wars generally; and hence you draw the farther inference, that A is also predicable of C, another particular case under the same class B. The inference here is, in the first instance, from part to whole; and finally, through that whole, from the one part to another part of the same whole. Induction includes in its major premiss all the particulars, declaring all of them to be severally subjects of the major as predicate; hence it infers as conclusion, that the major is also predicable of the middle or class-term comprising all these particulars, but comprising no others. Example includes not all, but only one or a few particulars; inferring from it or them, first, to the entire class, next, to some new analogous particular belonging to the class.58

57 Ibid. II. xxiv. p. 68, b. 38: παραδεῖγμα δ’ ἐστὶν ὅταν τῷ μέσῳ τὸ ἄκρον ὑπάρχον δειχθῇ διὰ τοῦ ὁμοίου τῷ τρίτῳ.

58 Analyt. Prior. II. xxiv. p. 69, a. 1-19. Julius Pacius (p. 400) notes the unauthorized character of this so-called Paradeigmatic Syllogism, contradicting the rules of the figures laid down by Aristotle, and also the confused manner in which the scope of it is described: first, to infer from a single example to the universal; next, to infer from a single example through the universal to another parallel case. To which we may add the confused description in p. 69, a. 17, 18, where τὸ ἄκρον in the first of the two lines signifies the major extreme — in the second of the two the minor extreme. See Waitz’s note, p. 533.

If we turn to ch. xxvii. p. 70, a. 30-34, we shall find Aristotle on a different occasion disallowing altogether this so-called Syllogism from Example.

These chapters respecting Induction and Example are among the most obscure and perplexing in the Aristotelian Analytica. The attempt to throw both Induction and Example into the syllogistic form is alike complicated and unfortunate; moreover, the unsatisfactory reading and diversities in the text, among commentators and translators, show that the reasoning of Aristotle has hitherto been imperfectly apprehended.59 From some of his phrases, we see that he was aware of the essential antithesis between Induction and Syllogism; yet the syllogistic forms appear to have exercised such fascination over his mind, that he could not be satisfied without trying to find some abnormal form of Syllogism to represent and give validity to Induction. In explaining generally what the Syllogism is, and what Induction is, he informs us that the Syllogism presupposes and rests upon the process of Induction as its postulate. For there can be no valid Syllogism without an universal proposition in one (at least) of the premisses; and he declares, unequivocally, that universal propositions are obtained only through Induction. How Induction operates through the particular facts of sense, remembered, compared, and coalescing into clusters held together by associating similarity, he has also told us; it is thus that Experience, with its universal notions and conjunctions, is obtained. But this important process is radically distinct from that of syllogizing, though it furnishes the basis upon which all syllogizing is built.

59 Sir W. Hamilton (Lectures on Logic, vol. i. p. 319) says justly, that Aristotle has been very brief and unexplicit in his treatment of Induction. Yet the objections that Hamilton makes to Aristotle are very different from those which I should make. In the learned and valuable Appendix to his Lectures (vol. iv. pp. 358-369), he collects various interesting criticisms of logicians respecting Induction as handled by Aristotle. Ramus (in his Scholæ Dialecticæ, VIII. xi.) says very truly:— “Quid vero sit Inductio, perobscure ab Aristotele declaratur; nec ab interpretibus intelligitur, quo modo syllogismus per medium concludat majus extremum de minore; inductio, majus de medio per minus.”

The Inductive Syllogism, as constructed by Aristotle, requires a reciprocating minor premiss. It may, indeed, be cited (as I have already remarked) in support of Hamilton’s favourite precept of quantifying the predicate. The predicate of this minor must be assumed as quantified in thought, the subject being taken as co-extensive therewith. Therefore Hamilton’s demand that it shall be quantified in speech has really in this case that foundation which he erroneously claims for it in all cases. He complains that Lambert and some other logicians dispense with the necessity of quantifying the predicate of the minor by making it disjunctive; and adds the remarkable statement that “the recent German logicians, Herbart, Twesten, Drobisch, &c., following Lambert, make the Inductive Syllogism a byeword” (p. 366). I agree with them in thinking the attempted transformation of Induction into Syllogism very unfortunate, though my reasons are probably not the same as theirs.

Trendelenburg agrees with those who said that Aristotle’s doctrine about the Inductive Syllogism required that the minor should be disjunctively enunciated (Logische Untersuchungen, xiv. p. 175, xvi. pp. 262, 263; also Erläuterungen zu den Elementen der Aristotelischen Logik, ss. 34-36, p. 71). Ueberweg takes a similar view (System der Logik, sect. 128, p. 367, 3rd ed.). If the Inductive Inference is to be twisted into Syllogism, it seems more naturally to fall into an hypothetical syllogism, e. g.:—

If this, that, and the other magnet attract iron, all magnets attract iron;
But this, that, and the other magnet do attract iron: Ergo, &c.

The central idea of the Syllogism, as defined by Aristotle, is that of a conclusion following from given premisses by necessary sequence;60 meaning by the term necessary thus much and no more — that you cannot grant the premisses, and deny the conclusion, without being inconsistent with yourself, or falling into contradiction. In all the various combinations of propositions, set forth by Aristotle as the different figures and modes of Syllogism, this property of necessary sequence is found. But it is a property which no Induction can ever possess.61 When Aristotle professes to point out a particular mode of Syllogism to which Induction conforms, he can only do so by falsifying the process of Induction, and by not accurately distinguishing between what is observed and what is inferred. In the case which he takes to illustrate the Inductive Syllogism — the inference from all particular bile-less animals to the whole class bile-less — he assumes that we have ascertained the attribute to belong to all the particulars, and that the inductive inference consists in passing from all of them to the class-term; the passage from premisses to conclusion being here necessary, and thus falling under the definition of Syllogism; since, to grant the premisses, and yet to deny the conclusion, involves a contradiction. But this doctrine misconceives what the inductive inference really is. We never can observe all the particulars of a class, which is indefinite as to number of particulars, and definite only in respect of the attributes connoted by the class-term. We can only observe some of the particulars, a greater or smaller proportion. Now it is in the transition from these to the totality of particulars, that the real inductive inference consists; not in the transition from the totality to the class-term which denotes that totality and connotes its determining common attribute. In fact, the distinction between the totality of particulars and the meaning of the class-term, is one not commonly attended to; though it is worthy of note in an analysis of the intellectual process, and is therefore brought to view by Aristotle. But he employs it incorrectly as an intermediate step to slur over the radical distinction between Induction and Syllogism. He subjoins:62— “You must conceive the minor term C (in the Inductive Syllogism) as composed of all the particulars; for Induction is through all of them.” You may say that Induction is through all the particulars, if you distinguish this totality from the class-term, and if you treat the class-term as the ultimate terminus ad quem. But the Induction must first travel to all the particulars; being forced to take start from a part only, and then to jump onward far enough to cover the indefinite unobserved remainder. This jump is the real Induction; and this can never be brought under the definition of Syllogism; for in the best and most certain Induction the sequence is never a necessary one: you may grant the premisses and deny the conclusion without contradicting yourself.